there is another explanation with the Thales Theorem (or maybe triangle intersection theorem in USA?).

When you have a line which cuts the two sides of a triangle and that is parallel to the third side then you have the same ratio everywhere :
c/sqrt(1+(b/a)²)= a/1 = b/(b/a)

(forgive my english it’s not my natural language … math neither !)

In France it’s called the Thales’ Theorem but in USA I think it’s called the Intercept Theorem and you can find details on

The story behind this is that Thales was the first able to calculate the Gizeh Pyramid height because he though there was the same relationship between his shadow and his height and the pyramid shadow and pyramid height, he considered that the sun rays were parallels so that the same ratio applied between his values and the pyramid ones. Nice story.

When the Pythagorean Theorem was rearranged , you exposed the slope,
Amazing to me. THIS is the kind of essence I’ve been searching for in
mathematics: Thank you Kalid.